Preference curve

If the specimen crystal is curved, there will be a range of positions where the diffraction conditions are satisfied even for a plane wave. The rocking curve is broadened. It is simple to reduce the effect of curvature by reducing the collimator aperture. For semiconductor crystals it is good practice never to mn rocking curves with a collimator size above 1 mm, and 0.5 mm is preferable. Curved specimens are common if a mismatched epilayer forms coherently on a substrate, then the substrate will bow to reduce the elastic strain. The effect is geometric and independent of the diffraction geometiy. Table 2.1 illustrates this effect. 

Figure 1 (a) Consumer preference curve for acidity (b) linear relationship for acidity descriptions and pH (c) consumer preference curve as a function of pH. 

Figure 2 Consumer preference curve for clove bouquet as a function of eugenol.

If homologous oil series other than n-alkanes are employed, a similar shape of preference curve for a given... 

All widely used measures of risk are related to the downside portion of the risk curve. In striving to minimize risk at low expectations, they rarely look at what happens on the upside. In other words, a risk averse decision maker will prefer curve 2 (Figure 12.8), while a risk taker will prefer curve 3. In reality, no decision maker is completely risk averse or completely risk taker. Therefore, some compromise like the one offered by curve 4 needs to be identified. Thus, some objective measure that will help identify this compromise is needed. If such a measure is constructed, the evaluation can be automated so that a decision maker does not have to consider and compare a large number of curves visually. Aseeri etal. (2004) discussed some measures and proposed others such as ... 

An interesting feature is however that there is a natural or spontaneous curvature that indicates the piefen ed. state of the inteifacial layer, which is nut necessarily the actual. state. The preferred Curv ature could be the one related to the R concept, i.e., physicochemical formulation effects, while the actual one would result from the emulsification process. The difference between the two is some kind of bending energy frustration, which by the way could be related to the concept of stability of the interfacial structure, and of the resulting emulsion. 

Watchmaker s forceps may be straight or curved to the individual s preference. Curved forceps are handy for the release of the membrane when folded under the ring and in tricky situations. 

People prefer curves. Why curves Well, sharp contours might convey a sense of threat Ban M. Neta, M. - Psychological Science, 2006). They are associated with negative emotions, whereas curved contours are linked with positive reactions, as symbols of continuity... 

A somewhat subtle point of difficulty is the following. Adsorption isotherms are quite often entirely reversible in that adsorption and desorption curves are identical. On the other hand, the solid will not generally be an equilibrium crystal and, in fact, will often have quite a heterogeneous surface. The quantities ys and ysv are therefore not very well defined as separate quantities. It seems preferable to regard t, which is well defined in the case of reversible adsorption, as simply the change in interfacial free energy and to leave its further identification to treatments accepted as modelistic. 

The integral under the heat capacity curve is an energy (or enthalpy as the case may be) and is more or less independent of the details of the model. The quasi-chemical treatment improved the heat capacity curve, making it sharper and narrower than the mean-field result, but it still remained finite at the critical point. Further improvements were made by Bethe with a second approximation, and by Kirkwood (1938). Figure A2.5.21 compares the various theoretical calculations [6]. These modifications lead to somewhat lower values of the critical temperature, which could be related to a flattening of the coexistence curve. Moreover, and perhaps more important, they show that a short-range order persists to higher temperatures, as it must because of the preference for unlike pairs the excess heat capacity shows a discontinuity, but it does not drop to zero as mean-field theories predict. Unfortunately these improvements are still analytic and in the vicinity of the critical point still yield a parabolic coexistence curve and a finite heat capacity just as the mean-field treatments do. 

For this reduction use preferably a i litre round-bottomed flask having 3 necks (Fig. 23(G), p. 46), the two necks at the flanks being straight (to avoid the obstruction, during the addition of sodium, which a curved neck might cause). Fit the central neck with a stirrer, one of the side necks with a reflux water-condenser, and the other with a glass or rubber stopper. 

The comparison plot offers a particularly simple and direct means of comparing the shapes of a pair of isotherms but for more general applications which involve a numt>er of samples of a solid covering a wide range of specific surface, the a,-method is preferable. The j-curve represents a convenient way of recording and using the reference isotherm. 

Everett concludes that in systems where pore blocking can occur, pore size distribution curves derived from the desorption branch of the isotherm are likely to give a misleading picture of the pore structure in particular the size distribution will appear to be much narrower than it actually is. Thus the adsorption branch is to be preferred unless network effects are known to be absent. 

Standardizations using a single standard are common, but also are subject to greater uncertainty. Whenever possible, a multiple-point standardization is preferred. The results of a multiple-point standardization are graphed as a calibration curve. A linear regression analysis can provide an equation for the standardization. 

Fig. 2. Young s modulus corrected for porosity as a function of preferred orientation curve is based on theoretical model where = rayon-based fibers Q — PAN-based fibers and A = pitch-based fibers (2). To convert GPa to psi, multiply by 145,000.

Theoretically based correlations (or semitheoretical extensions of them), rooted in thermodynamics or other fundamentals are ordinarily preferred. However, rigorous theoretical understanding of real systems is far from complete, and purely empirical correlations typically have strict limits on apphcabihty. Many correlations result from curve-fitting the desired parameter to an appropriate independent variable. Some fitting exercises are rooted in theory, eg, Antoine s equation for vapor pressure others can be described as being semitheoretical. These distinctions usually do not refer to adherence to the observations of natural systems, but rather to the agreement in form to mathematical models of idealized systems. The advent of readily available computers has revolutionized the development and use of correlation techniques (see Chemometrics Computer technology Dimensional analysis). 

Since the utility curve has such a subjective basis, most companies prefer the objectivity of (NPV) and (DCFRR) over the range of the normal income and expenditure budget. Subjective methods tend to be reserved for exceptionally high risk projects. 

Because of the time and expense involved in conducting laboratoiy distillation tests of all three basic types, it has become increasingly common to use empirical correlations to estimate the other two distillation curves when either the ASTM, TBP, or EFN- curve is available. Preferred correlations given in the API Technical Data Book—Petroleum Refining (op. dt.) are based on the work of Edmister and Pollock [Chem. Eng. Prog., 44, 905 (1948)], Edmister and Okamoto [Pet. Refiner, 38(8), 117 (1959) 38(9), 271 (1959)], Maxwell Data Book on... 

It is always preferable to plot data so that the area under the frequency curve is normalized to 100 percent since this facilitates data comparison. 

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